The results of a study on the evolution of HiPco single-walled carbon nanotubes during the oxidizing action of H2SO4 and HNO3 are presented. The process conditions used have been chosen so as to avoid any significant damage to the nanotube structure. The type and level of functionalization, the location of the grafted functions on the surface of the nanotube and the changes in morphological characteristics of the samples were examined by using a wide and complementary range of analytical techniques. We propose an explanation for the differences in the oxidizing action of sulfuric and nitric acids. The combined results allow us to suggest possible reaction mechanisms that occur on the surface of the nanotube.